/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([-2, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([79, 79, -w - 9]) primes_array = [ [2, 2, -w],\ [7, 7, -2*w + 1],\ [7, 7, -2*w - 1],\ [9, 3, 3],\ [17, 17, 3*w + 1],\ [17, 17, 3*w - 1],\ [23, 23, w + 5],\ [23, 23, -w + 5],\ [25, 5, 5],\ [31, 31, 4*w + 1],\ [31, 31, -4*w + 1],\ [41, 41, 2*w - 7],\ [41, 41, -2*w - 7],\ [47, 47, -w - 7],\ [47, 47, w - 7],\ [71, 71, -6*w - 1],\ [71, 71, 6*w - 1],\ [73, 73, -7*w - 5],\ [73, 73, 7*w - 5],\ [79, 79, -w - 9],\ [79, 79, w - 9],\ [89, 89, -4*w - 11],\ [89, 89, 4*w - 11],\ [97, 97, -7*w - 1],\ [97, 97, 7*w - 1],\ [103, 103, -3*w - 11],\ [103, 103, 3*w - 11],\ [113, 113, 2*w - 11],\ [113, 113, -2*w - 11],\ [121, 11, -11],\ [127, 127, -8*w - 1],\ [127, 127, 8*w - 1],\ [137, 137, 4*w - 13],\ [137, 137, -4*w - 13],\ [151, 151, 3*w - 13],\ [151, 151, -3*w - 13],\ [167, 167, -w - 13],\ [167, 167, w - 13],\ [169, 13, -13],\ [191, 191, 10*w - 3],\ [191, 191, -10*w - 3],\ [193, 193, -4*w - 15],\ [193, 193, 4*w - 15],\ [199, 199, -10*w - 1],\ [199, 199, 10*w - 1],\ [223, 223, -w - 15],\ [223, 223, w - 15],\ [233, 233, -11*w - 3],\ [233, 233, 11*w - 3],\ [239, 239, -5*w - 17],\ [239, 239, 5*w - 17],\ [241, 241, -11*w - 1],\ [241, 241, 11*w - 1],\ [257, 257, 4*w - 17],\ [257, 257, -4*w - 17],\ [263, 263, 7*w - 19],\ [263, 263, -7*w - 19],\ [271, 271, -3*w - 17],\ [271, 271, 3*w - 17],\ [281, 281, 2*w - 17],\ [281, 281, -2*w - 17],\ [311, 311, -5*w - 19],\ [311, 311, 5*w - 19],\ [313, 313, -8*w - 21],\ [313, 313, 8*w - 21],\ [337, 337, -13*w - 1],\ [337, 337, 13*w - 1],\ [353, 353, 2*w - 19],\ [353, 353, -2*w - 19],\ [359, 359, -w - 19],\ [359, 359, w - 19],\ [361, 19, -19],\ [367, 367, 9*w - 23],\ [367, 367, -9*w - 23],\ [383, 383, -14*w - 3],\ [383, 383, 14*w - 3],\ [401, 401, -8*w - 23],\ [401, 401, 8*w - 23],\ [409, 409, -17*w - 13],\ [409, 409, 17*w - 13],\ [431, 431, -7*w - 23],\ [431, 431, 7*w - 23],\ [433, 433, 2*w - 21],\ [433, 433, -2*w - 21],\ [439, 439, -w - 21],\ [439, 439, w - 21],\ [449, 449, -15*w - 1],\ [449, 449, 15*w - 1],\ [457, 457, -6*w - 23],\ [457, 457, 6*w - 23],\ [463, 463, 9*w - 25],\ [463, 463, -9*w - 25],\ [479, 479, -18*w - 13],\ [479, 479, 18*w - 13],\ [487, 487, 16*w - 5],\ [487, 487, -16*w - 5],\ [503, 503, 16*w - 3],\ [503, 503, -16*w - 3],\ [521, 521, 2*w - 23],\ [521, 521, -2*w - 23],\ [569, 569, -17*w - 3],\ [569, 569, 17*w - 3],\ [577, 577, -17*w - 1],\ [577, 577, 17*w - 1],\ [593, 593, 4*w - 25],\ [593, 593, -4*w - 25],\ [599, 599, -11*w - 29],\ [599, 599, 11*w - 29],\ [601, 601, 8*w - 27],\ [601, 601, -8*w - 27],\ [607, 607, 3*w - 25],\ [607, 607, -3*w - 25],\ [617, 617, 2*w - 25],\ [617, 617, -2*w - 25],\ [631, 631, -7*w - 27],\ [631, 631, 7*w - 27],\ [641, 641, -10*w - 29],\ [641, 641, 10*w - 29],\ [647, 647, -18*w - 1],\ [647, 647, 18*w - 1],\ [673, 673, -12*w - 31],\ [673, 673, 12*w - 31],\ [719, 719, 11*w - 31],\ [719, 719, -11*w - 31],\ [727, 727, -w - 27],\ [727, 727, w - 27],\ [743, 743, 7*w - 29],\ [743, 743, -7*w - 29],\ [751, 751, 13*w - 33],\ [751, 751, -13*w - 33],\ [761, 761, 10*w - 31],\ [761, 761, -10*w - 31],\ [769, 769, 23*w - 17],\ [769, 769, -23*w - 17],\ [809, 809, 4*w - 29],\ [809, 809, -4*w - 29],\ [823, 823, -3*w - 29],\ [823, 823, 3*w - 29],\ [839, 839, -w - 29],\ [839, 839, w - 29],\ [841, 29, -29],\ [857, 857, 21*w - 5],\ [857, 857, -21*w - 5],\ [863, 863, 24*w - 17],\ [863, 863, -24*w - 17],\ [881, 881, -21*w - 1],\ [881, 881, 21*w - 1],\ [887, 887, 13*w - 35],\ [887, 887, -13*w - 35],\ [911, 911, 26*w + 21],\ [911, 911, -26*w + 21],\ [919, 919, 22*w - 7],\ [919, 919, -22*w - 7],\ [929, 929, -4*w - 31],\ [929, 929, 4*w - 31],\ [937, 937, -12*w - 35],\ [937, 937, 12*w - 35],\ [953, 953, 2*w - 31],\ [953, 953, -2*w - 31],\ [967, 967, -22*w - 1],\ [967, 967, 22*w - 1],\ [977, 977, -14*w - 37],\ [977, 977, 14*w - 37],\ [983, 983, -11*w - 35],\ [983, 983, 11*w - 35],\ [991, 991, -26*w - 19],\ [991, 991, 26*w - 19],\ [1009, 1009, -23*w - 7],\ [1009, 1009, 23*w - 7],\ [1031, 1031, 13*w - 37],\ [1031, 1031, -13*w - 37],\ [1033, 1033, 23*w - 5],\ [1033, 1033, -23*w - 5],\ [1039, 1039, 5*w - 33],\ [1039, 1039, -5*w - 33],\ [1049, 1049, -23*w - 3],\ [1049, 1049, 23*w - 3],\ [1063, 1063, -9*w - 35],\ [1063, 1063, 9*w - 35],\ [1087, 1087, -w - 33],\ [1087, 1087, w - 33],\ [1097, 1097, -27*w - 19],\ [1097, 1097, 27*w - 19],\ [1103, 1103, -24*w - 7],\ [1103, 1103, 24*w - 7],\ [1129, 1129, -14*w - 39],\ [1129, 1129, 14*w - 39],\ [1151, 1151, -24*w - 1],\ [1151, 1151, 24*w - 1],\ [1153, 1153, -6*w - 35],\ [1153, 1153, 6*w - 35],\ [1193, 1193, -4*w - 35],\ [1193, 1193, 4*w - 35],\ [1201, 1201, 25*w - 7],\ [1201, 1201, -25*w - 7],\ [1217, 1217, 2*w - 35],\ [1217, 1217, -2*w - 35],\ [1223, 1223, -w - 35],\ [1223, 1223, w - 35],\ [1231, 1231, -15*w - 41],\ [1231, 1231, 15*w - 41],\ [1249, 1249, -25*w - 1],\ [1249, 1249, 25*w - 1],\ [1279, 1279, 11*w - 39],\ [1279, 1279, -11*w - 39],\ [1289, 1289, -14*w - 41],\ [1289, 1289, 14*w - 41],\ [1297, 1297, 31*w + 25],\ [1297, 1297, -31*w + 25],\ [1303, 1303, 26*w - 7],\ [1303, 1303, -26*w - 7],\ [1319, 1319, -5*w - 37],\ [1319, 1319, 5*w - 37],\ [1321, 1321, -10*w - 39],\ [1321, 1321, 10*w - 39],\ [1327, 1327, 26*w - 5],\ [1327, 1327, -26*w - 5],\ [1361, 1361, 2*w - 37],\ [1361, 1361, -2*w - 37],\ [1367, 1367, -w - 37],\ [1367, 1367, w - 37],\ [1369, 37, -37],\ [1399, 1399, 15*w - 43],\ [1399, 1399, -15*w - 43],\ [1409, 1409, -27*w - 7],\ [1409, 1409, 27*w - 7],\ [1423, 1423, -32*w - 25],\ [1423, 1423, 32*w - 25],\ [1433, 1433, -27*w - 5],\ [1433, 1433, 27*w - 5],\ [1439, 1439, -11*w - 41],\ [1439, 1439, 11*w - 41],\ [1447, 1447, -17*w - 45],\ [1447, 1447, 17*w - 45],\ [1471, 1471, -5*w - 39],\ [1471, 1471, 5*w - 39],\ [1481, 1481, 10*w - 41],\ [1481, 1481, -10*w - 41],\ [1487, 1487, 28*w - 9],\ [1487, 1487, -28*w - 9],\ [1489, 1489, -4*w - 39],\ [1489, 1489, 4*w - 39],\ [1511, 1511, -13*w - 43],\ [1511, 1511, 13*w - 43],\ [1543, 1543, 28*w - 5],\ [1543, 1543, -28*w - 5],\ [1553, 1553, -33*w - 25],\ [1553, 1553, 33*w - 25],\ [1559, 1559, 28*w - 3],\ [1559, 1559, -28*w - 3],\ [1567, 1567, -28*w - 1],\ [1567, 1567, 28*w - 1],\ [1583, 1583, -34*w + 27],\ [1583, 1583, 34*w + 27],\ [1601, 1601, -29*w - 9],\ [1601, 1601, 29*w - 9],\ [1607, 1607, -11*w - 43],\ [1607, 1607, 11*w - 43],\ [1609, 1609, -6*w - 41],\ [1609, 1609, 6*w - 41],\ [1657, 1657, -29*w - 5],\ [1657, 1657, 29*w - 5],\ [1663, 1663, -3*w - 41],\ [1663, 1663, 3*w - 41],\ [1697, 1697, -16*w - 47],\ [1697, 1697, 16*w - 47],\ [1721, 1721, -35*w - 27],\ [1721, 1721, 35*w - 27],\ [1753, 1753, 18*w - 49],\ [1753, 1753, -18*w - 49],\ [1759, 1759, -15*w - 47],\ [1759, 1759, 15*w - 47],\ [1777, 1777, 6*w - 43],\ [1777, 1777, -6*w - 43],\ [1783, 1783, 11*w - 45],\ [1783, 1783, -11*w - 45],\ [1801, 1801, -20*w - 51],\ [1801, 1801, 20*w - 51],\ [1823, 1823, 17*w - 49],\ [1823, 1823, -17*w - 49],\ [1831, 1831, 3*w - 43],\ [1831, 1831, -3*w - 43],\ [1847, 1847, -w - 43],\ [1847, 1847, w - 43],\ [1849, 43, -43],\ [1871, 1871, 13*w - 47],\ [1871, 1871, -13*w - 47],\ [1873, 1873, -31*w - 7],\ [1873, 1873, 31*w - 7],\ [1879, 1879, 19*w - 51],\ [1879, 1879, -19*w - 51],\ [1889, 1889, 16*w - 49],\ [1889, 1889, -16*w - 49],\ [1913, 1913, 31*w - 3],\ [1913, 1913, -31*w - 3],\ [1951, 1951, 15*w - 49],\ [1951, 1951, -15*w - 49],\ [1993, 1993, 4*w - 45],\ [1993, 1993, -4*w - 45],\ [1999, 1999, 32*w - 7],\ [1999, 1999, -32*w - 7],\ [2017, 2017, 2*w - 45],\ [2017, 2017, -2*w - 45],\ [2039, 2039, -32*w - 3],\ [2039, 2039, 32*w - 3],\ [2063, 2063, 13*w - 49],\ [2063, 2063, -13*w - 49],\ [2081, 2081, -39*w + 31],\ [2081, 2081, 39*w + 31],\ [2087, 2087, -19*w - 53],\ [2087, 2087, 19*w - 53],\ [2089, 2089, -16*w - 51],\ [2089, 2089, 16*w - 51],\ [2111, 2111, 7*w - 47],\ [2111, 2111, -7*w - 47],\ [2113, 2113, 12*w - 49],\ [2113, 2113, -12*w - 49],\ [2129, 2129, 33*w - 7],\ [2129, 2129, -33*w - 7],\ [2137, 2137, -6*w - 47],\ [2137, 2137, 6*w - 47],\ [2143, 2143, -21*w - 55],\ [2143, 2143, 21*w - 55],\ [2153, 2153, 33*w - 5],\ [2153, 2153, -33*w - 5],\ [2161, 2161, -18*w - 53],\ [2161, 2161, 18*w - 53],\ [2207, 2207, -w - 47],\ [2207, 2207, w - 47],\ [2239, 2239, 40*w - 31],\ [2239, 2239, -40*w - 31],\ [2273, 2273, 8*w - 49],\ [2273, 2273, -8*w - 49],\ [2281, 2281, -22*w - 57],\ [2281, 2281, 22*w - 57],\ [2287, 2287, -34*w - 5],\ [2287, 2287, 34*w - 5],\ [2297, 2297, -16*w - 53],\ [2297, 2297, 16*w - 53],\ [2311, 2311, -34*w - 1],\ [2311, 2311, 34*w - 1],\ [2351, 2351, -5*w - 49],\ [2351, 2351, 5*w - 49],\ [2377, 2377, 18*w - 55],\ [2377, 2377, -18*w - 55],\ [2383, 2383, 3*w - 49],\ [2383, 2383, -3*w - 49],\ [2393, 2393, 2*w - 49],\ [2393, 2393, -2*w - 49],\ [2399, 2399, -w - 49],\ [2399, 2399, w - 49],\ [2417, 2417, -14*w - 53],\ [2417, 2417, 14*w - 53],\ [2423, 2423, -23*w - 59],\ [2423, 2423, 23*w - 59],\ [2441, 2441, -35*w - 3],\ [2441, 2441, 35*w - 3],\ [2447, 2447, -17*w - 55],\ [2447, 2447, 17*w - 55],\ [2473, 2473, 8*w - 51],\ [2473, 2473, -8*w - 51],\ [2503, 2503, -7*w - 51],\ [2503, 2503, 7*w - 51],\ [2521, 2521, -41*w - 29],\ [2521, 2521, 41*w - 29],\ [2543, 2543, 36*w - 7],\ [2543, 2543, -36*w - 7],\ [2551, 2551, 5*w - 51],\ [2551, 2551, -5*w - 51],\ [2591, 2591, -36*w - 1],\ [2591, 2591, 36*w - 1],\ [2593, 2593, 2*w - 51],\ [2593, 2593, -2*w - 51],\ [2609, 2609, 43*w - 33],\ [2609, 2609, -43*w - 33],\ [2617, 2617, 37*w - 11],\ [2617, 2617, -37*w - 11],\ [2633, 2633, -14*w - 55],\ [2633, 2633, 14*w - 55],\ [2647, 2647, -44*w + 35],\ [2647, 2647, 44*w + 35],\ [2657, 2657, 37*w - 9],\ [2657, 2657, -37*w - 9],\ [2663, 2663, -23*w - 61],\ [2663, 2663, 23*w - 61],\ [2671, 2671, 17*w - 57],\ [2671, 2671, -17*w - 57],\ [2687, 2687, -13*w - 55],\ [2687, 2687, 13*w - 55],\ [2689, 2689, -37*w - 7],\ [2689, 2689, 37*w - 7],\ [2711, 2711, 7*w - 53],\ [2711, 2711, -7*w - 53],\ [2713, 2713, -37*w - 5],\ [2713, 2713, 37*w - 5],\ [2719, 2719, 25*w - 63],\ [2719, 2719, -25*w - 63],\ [2729, 2729, 37*w - 3],\ [2729, 2729, -37*w - 3],\ [2753, 2753, -22*w - 61],\ [2753, 2753, 22*w - 61],\ [2767, 2767, -38*w - 11],\ [2767, 2767, 38*w - 11],\ [2777, 2777, 4*w - 53],\ [2777, 2777, -4*w - 53],\ [2791, 2791, -3*w - 53],\ [2791, 2791, 3*w - 53],\ [2801, 2801, 2*w - 53],\ [2801, 2801, -2*w - 53],\ [2809, 53, -53],\ [2833, 2833, -18*w - 59],\ [2833, 2833, 18*w - 59],\ [2857, 2857, 14*w - 57],\ [2857, 2857, -14*w - 57],\ [2879, 2879, -38*w - 3],\ [2879, 2879, 38*w - 3],\ [2887, 2887, -38*w - 1],\ [2887, 2887, 38*w - 1],\ [2897, 2897, -8*w - 55],\ [2897, 2897, 8*w - 55],\ [2903, 2903, -17*w - 59],\ [2903, 2903, 17*w - 59],\ [2927, 2927, -7*w - 55],\ [2927, 2927, 7*w - 55],\ [2953, 2953, 6*w - 55],\ [2953, 2953, -6*w - 55],\ [2969, 2969, 16*w - 59],\ [2969, 2969, -16*w - 59],\ [2999, 2999, 19*w - 61],\ [2999, 2999, -19*w - 61],\ [3001, 3001, 22*w - 63],\ [3001, 3001, -22*w - 63],\ [3023, 3023, -w - 55],\ [3023, 3023, w - 55],\ [3041, 3041, -39*w - 1],\ [3041, 3041, 39*w - 1],\ [3049, 3049, -47*w - 37],\ [3049, 3049, 47*w - 37],\ [3079, 3079, -40*w - 11],\ [3079, 3079, 40*w - 11],\ [3089, 3089, 14*w - 59],\ [3089, 3089, -14*w - 59],\ [3119, 3119, -40*w - 9],\ [3119, 3119, 40*w - 9],\ [3121, 3121, 8*w - 57],\ [3121, 3121, -8*w - 57],\ [3137, 3137, 26*w - 67],\ [3137, 3137, -26*w - 67],\ [3167, 3167, -23*w - 65],\ [3167, 3167, 23*w - 65],\ [3169, 3169, 20*w - 63],\ [3169, 3169, -20*w - 63],\ [3191, 3191, 40*w - 3],\ [3191, 3191, -40*w - 3],\ [3209, 3209, 16*w - 61],\ [3209, 3209, -16*w - 61],\ [3217, 3217, 4*w - 57],\ [3217, 3217, -4*w - 57],\ [3257, 3257, -22*w - 65],\ [3257, 3257, 22*w - 65],\ [3271, 3271, 15*w - 61],\ [3271, 3271, -15*w - 61],\ [3313, 3313, -41*w - 7],\ [3313, 3313, 41*w - 7],\ [3319, 3319, 9*w - 59],\ [3319, 3319, -9*w - 59],\ [3329, 3329, -47*w - 33],\ [3329, 3329, 47*w - 33],\ [3343, 3343, -21*w - 65],\ [3343, 3343, 21*w - 65],\ [3359, 3359, -42*w - 13],\ [3359, 3359, 42*w - 13],\ [3361, 3361, -41*w - 1],\ [3361, 3361, 41*w - 1],\ [3391, 3391, -17*w - 63],\ [3391, 3391, 17*w - 63],\ [3407, 3407, 42*w - 11],\ [3407, 3407, -42*w - 11],\ [3433, 3433, -49*w - 37],\ [3433, 3433, 49*w - 37],\ [3449, 3449, -4*w - 59],\ [3449, 3449, 4*w - 59],\ [3457, 3457, -16*w - 63],\ [3457, 3457, 16*w - 63],\ [3463, 3463, -3*w - 59],\ [3463, 3463, 3*w - 59],\ [3481, 59, -59],\ [3511, 3511, 25*w - 69],\ [3511, 3511, -25*w - 69],\ [3527, 3527, -42*w - 1],\ [3527, 3527, 42*w - 1],\ [3529, 3529, -43*w - 13],\ [3529, 3529, 43*w - 13],\ [3559, 3559, 9*w - 61],\ [3559, 3559, -9*w - 61],\ [3583, 3583, 27*w - 71],\ [3583, 3583, -27*w - 71],\ [3593, 3593, -8*w - 61],\ [3593, 3593, 8*w - 61],\ [3607, 3607, -21*w - 67],\ [3607, 3607, 21*w - 67],\ [3617, 3617, 43*w - 9],\ [3617, 3617, -43*w - 9],\ [3623, 3623, 7*w - 61],\ [3623, 3623, -7*w - 61],\ [3631, 3631, -50*w - 37],\ [3631, 3631, 50*w - 37],\ [3671, 3671, 5*w - 61],\ [3671, 3671, -5*w - 61],\ [3673, 3673, 43*w - 5],\ [3673, 3673, -43*w - 5],\ [3697, 3697, -43*w - 1],\ [3697, 3697, 43*w - 1],\ [3719, 3719, -w - 61],\ [3719, 3719, w - 61],\ [3721, 61, -61],\ [3727, 3727, 52*w - 41],\ [3727, 3727, -52*w - 41],\ [3761, 3761, 28*w - 73],\ [3761, 3761, -28*w - 73],\ [3767, 3767, 19*w - 67],\ [3767, 3767, -19*w - 67],\ [3769, 3769, -10*w - 63],\ [3769, 3769, 10*w - 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19],\ [8887, 8887, -68*w - 19],\ [8929, 8929, 67*w - 7],\ [8929, 8929, -67*w - 7],\ [8951, 8951, 25*w - 101],\ [8951, 8951, -25*w - 101],\ [8969, 8969, 67*w - 3],\ [8969, 8969, -67*w - 3],\ [8999, 8999, -35*w - 107],\ [8999, 8999, 35*w - 107],\ [9001, 9001, 79*w - 59],\ [9001, 9001, -79*w - 59],\ [9007, 9007, -3*w - 95],\ [9007, 9007, 3*w - 95],\ [9041, 9041, 28*w - 103],\ [9041, 9041, -28*w - 103],\ [9049, 9049, 24*w - 101],\ [9049, 9049, -24*w - 101],\ [9103, 9103, 31*w - 105],\ [9103, 9103, -31*w - 105],\ [9127, 9127, -68*w - 11],\ [9127, 9127, 68*w - 11],\ [9137, 9137, 34*w - 107],\ [9137, 9137, -34*w - 107],\ [9151, 9151, -27*w - 103],\ [9151, 9151, 27*w - 103],\ [9161, 9161, 69*w - 19],\ [9161, 9161, -69*w - 19],\ [9199, 9199, 68*w - 7],\ [9199, 9199, -68*w - 7],\ [9209, 9209, 10*w - 97],\ [9209, 9209, -10*w - 97],\ [9239, 9239, -68*w - 3],\ [9239, 9239, 68*w - 3],\ [9241, 9241, -42*w - 113],\ [9241, 9241, 42*w - 113],\ [9257, 9257, -26*w - 103],\ [9257, 9257, 26*w - 103],\ [9281, 9281, 8*w - 97],\ [9281, 9281, -8*w - 97],\ [9311, 9311, -7*w - 97],\ [9311, 9311, 7*w - 97],\ [9319, 9319, -80*w - 59],\ [9319, 9319, 80*w - 59],\ [9337, 9337, 6*w - 97],\ [9337, 9337, -6*w - 97],\ [9343, 9343, -29*w - 105],\ [9343, 9343, 29*w - 105],\ [9377, 9377, 4*w - 97],\ [9377, 9377, -4*w - 97],\ [9391, 9391, 3*w - 97],\ [9391, 9391, -3*w - 97],\ [9431, 9431, 35*w - 109],\ [9431, 9431, -35*w - 109],\ [9433, 9433, -38*w - 111],\ [9433, 9433, 38*w - 111],\ [9439, 9439, 70*w - 19],\ [9439, 9439, -70*w - 19],\ [9463, 9463, 13*w - 99],\ [9463, 9463, -13*w - 99],\ [9473, 9473, -69*w - 7],\ [9473, 9473, 69*w - 7],\ [9479, 9479, 82*w - 63],\ [9479, 9479, -82*w - 63],\ [9497, 9497, -69*w - 5],\ [9497, 9497, 69*w - 5],\ [9511, 9511, -70*w - 17],\ [9511, 9511, 70*w - 17],\ [9521, 9521, -69*w - 1],\ [9521, 9521, 69*w - 1],\ [9551, 9551, 80*w - 57],\ [9551, 9551, -80*w - 57],\ [9601, 9601, -10*w - 99],\ [9601, 9601, 10*w - 99],\ [9623, 9623, -84*w + 67],\ [9623, 9623, 84*w + 67],\ [9631, 9631, -70*w - 13],\ [9631, 9631, 70*w - 13],\ [9649, 9649, -30*w - 107],\ [9649, 9649, 30*w - 107],\ [9679, 9679, 70*w - 11],\ [9679, 9679, -70*w - 11],\ [9689, 9689, -16*w - 101],\ [9689, 9689, 16*w - 101],\ [9697, 9697, 42*w - 115],\ [9697, 9697, -42*w - 115],\ [9719, 9719, 70*w - 9],\ [9719, 9719, -70*w - 9],\ [9721, 9721, -71*w - 19],\ [9721, 9721, 71*w - 19],\ [9743, 9743, -47*w - 119],\ [9743, 9743, 47*w - 119],\ [9767, 9767, -29*w - 107],\ [9767, 9767, 29*w - 107],\ [9769, 9769, -4*w - 99],\ [9769, 9769, 4*w - 99],\ [9791, 9791, 70*w - 3],\ [9791, 9791, -70*w - 3],\ [9817, 9817, -44*w - 117],\ [9817, 9817, 44*w - 117],\ [9833, 9833, 32*w - 109],\ [9833, 9833, -32*w - 109],\ [9839, 9839, -49*w - 121],\ [9839, 9839, 49*w - 121],\ [9857, 9857, -71*w - 15],\ [9857, 9857, 71*w - 15],\ [9871, 9871, 35*w - 111],\ [9871, 9871, -35*w - 111],\ [9887, 9887, 84*w - 65],\ [9887, 9887, -84*w - 65],\ [9929, 9929, -46*w - 119],\ [9929, 9929, 46*w - 119],\ [9967, 9967, 82*w - 59],\ [9967, 9967, -82*w - 59]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^3 + x^2 - 5*x - 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -e + 1, -1/2*e^2 + 5/2, -1/2*e^2 - 2*e + 1/2, -2, 1/2*e^2 + 2*e - 5/2, -2*e^2 - 2*e + 8, 5/2*e^2 + 2*e - 9/2, -e^2 + e + 2, e^2 + 2*e - 3, 3/2*e^2 - 3/2, e^2 - 3*e - 8, 2*e^2 + 4*e - 8, 2*e + 2, 2*e + 2, -5/2*e^2 - 4*e + 13/2, 3*e^2 - 15, 1/2*e^2 - 1/2, 5/2*e^2 + 4*e - 1/2, -1, -3*e^2 - 2*e + 13, -9/2*e^2 - 4*e + 25/2, 5/2*e^2 - 2*e - 33/2, 2*e - 8, -3*e^2 - 2*e + 11, -9/2*e^2 - 6*e + 25/2, 5*e - 1, -3*e^2 - 2*e + 7, 3*e^2 + 3*e - 12, -6*e^2 - 6*e + 14, e^2 + 8*e - 5, -3*e^2 - 2*e + 21, -e^2 - 2*e + 13, -e^2 + 6*e + 9, -e^2 - 8*e + 5, -2*e^2 + 4*e + 18, -4*e^2 - 4*e + 16, 4*e^2 + 8*e - 12, -e^2 - 2*e + 5, -3/2*e^2 - 8*e - 1/2, 3*e - 7, 13/2*e^2 - 49/2, 5*e^2 + 4*e - 23, 4*e^2 + 10*e - 6, e^2 - 6*e - 11, 2*e^2 + 4*e - 6, -1/2*e^2 + 2*e + 45/2, -3/2*e^2 + 15/2, -3*e^2 - 8*e + 5, -2*e^2 - 11*e + 1, 2*e^2 + 6*e + 4, 6*e + 4, 7*e^2 + 6*e - 19, -e^2 - 2*e - 7, -3*e^2 + 25, e^2 - 2*e - 19, 17/2*e^2 + 2*e - 57/2, -3/2*e^2 + 6*e + 35/2, 6*e^2 - e - 29, -3/2*e^2 - 8*e - 1/2, -1/2*e^2 - 2*e + 45/2, 5*e^2 - 4*e - 21, -3*e^2 - 2*e + 5, -2*e^2 - 6*e + 30, -4*e^2 - 2*e + 16, -e^2 - 2*e + 13, -7*e^2 - 14*e + 23, 8*e - 10, 4*e - 18, -9*e^2 - 16*e + 29, -3/2*e^2 - 2*e + 19/2, 5*e^2 + 14*e - 25, -e^2 - 12*e - 7, -e^2 + 8*e + 13, 5*e - 21, 5*e^2 + 10*e - 11, 15/2*e^2 + 6*e - 47/2, -2*e^2 - 4*e + 12, -10*e^2 + 40, 4*e^2 + 8*e - 10, 1/2*e^2 + 4*e + 51/2, -e^2 + 2*e - 5, -3/2*e^2 + 2*e + 43/2, -3/2*e^2 + 4*e + 11/2, -2*e^2 - 4*e + 10, -5/2*e^2 + 2*e + 53/2, -10*e, -7/2*e^2 + 8*e + 35/2, 6*e^2 + 6*e - 14, -4*e^2 - 16*e + 22, -13/2*e^2 - 18*e + 33/2, 2*e^2 - e - 21, -3/2*e^2 - 14*e + 11/2, -3*e^2 - 2*e + 13, -13/2*e^2 - 8*e + 61/2, -6*e^2 + 22, e^2 - 6*e - 27, e^2 - 10*e + 5, 5*e^2 + 4*e - 15, 3*e^2 - 6*e - 27, -7*e^2 - 14*e + 35, 7*e^2 + 6*e - 11, -9*e^2 - 2*e + 45, -e^2 - 10*e - 3, -4*e^2 - 18*e + 24, 6*e^2 + 18*e - 34, -6*e^2 - 14*e + 16, -4*e^2 - 4*e + 8, 9*e^2 + 8*e - 23, 1/2*e^2 - 2*e - 13/2, 6*e^2 + 7*e - 17, 3/2*e^2 - 4*e - 7/2, -5/2*e^2 + 6*e + 65/2, 7/2*e^2 - 2*e + 25/2, -9/2*e^2 - 2*e + 77/2, 2*e^2 + 12*e - 22, -11*e^2 - 2*e + 47, 7*e^2 - 2*e - 15, -1/2*e^2 + 2*e + 13/2, 4*e^2 + 9*e - 25, 3*e^2 + 6*e - 11, 5/2*e^2 + 10*e + 3/2, 4*e^2 + 16*e - 4, 5*e^2 + 18*e - 19, -2*e^2 - 4*e + 38, 3*e^2 + 1, 6*e^2 + 13*e - 19, 4*e^2 + 12*e - 28, 9/2*e^2 - 8*e - 9/2, 10*e + 22, -9*e^2 - 5*e + 28, 3*e^2 - 9*e - 28, 19/2*e^2 + 18*e - 59/2, -e^2 - 18*e - 7, 4*e - 2, -7*e^2 - e + 26, 9*e^2 + 16*e - 45, 4*e^2 + 2*e + 22, 2*e^2 - 9*e - 21, -4*e^2 + 2*e - 10, 15*e^2 + 24*e - 45, 3*e^2 - 11*e - 6, -7*e^2 - 5*e + 26, 31/2*e^2 + 14*e - 55/2, 7*e^2 + 10*e - 49, 11*e^2 + 14*e - 39, e^2 - 9*e - 10, 7*e^2 - 6*e - 17, 6*e^2 + 9*e - 43, -5*e^2 + 6*e + 39, -6*e^2 - 17*e + 7, -7/2*e^2 - 4*e - 53/2, -11*e^2 + 39, -17/2*e^2 - 20*e + 33/2, -3*e^2 + 18*e + 23, 7/2*e^2 + 16*e - 63/2, -13*e^2 - 26*e + 53, 11*e^2 - 3*e - 46, -e^2 - 17*e + 4, 5/2*e^2 + 2*e + 19/2, -4*e^2 + 12*e + 8, -11/2*e^2 - 8*e + 23/2, e^2 + 12*e - 27, 5/2*e^2 - 6*e - 41/2, -14*e^2 - 17*e + 31, 9*e^2 - 2*e - 23, e^2 + 2*e + 17, -7*e^2 - 8*e + 17, -1/2*e^2 - 4*e - 47/2, 23/2*e^2 + 18*e - 91/2, -7*e^2 - 2*e + 41, -23/2*e^2 - 14*e + 19/2, -3*e^2 + 4*e + 49, 5/2*e^2 - 16*e - 9/2, -9*e^2 - 12*e + 57, 12*e^2 + 6*e - 36, 11*e^2 - 4*e - 57, 10*e^2 + 12*e - 42, 1/2*e^2 - 12*e - 9/2, -9*e^2 + 10*e + 59, 9*e^2 - 13, 15/2*e^2 - 8*e - 71/2, 6*e^2 + 18*e - 10, 4*e^2 + 8*e + 24, 2*e^2 - 11*e + 9, 14*e^2 + 14*e - 58, 2*e^2 + 8*e - 12, e^2 - 2*e + 9, -19/2*e^2 - 2*e + 67/2, -8*e^2 - 6*e + 44, 15*e^2 + 27*e - 52, 1/2*e^2 + 4*e + 35/2, -31/2*e^2 - 14*e + 71/2, -14*e^2 - 8*e + 52, 8*e - 2, 8*e - 26, 14*e^2 - 2*e - 42, -12*e^2 - 11*e + 35, -12*e^2 - 14*e + 14, -4*e^2 + 2*e + 2, 4*e^2 - 8*e - 20, 9*e^2 - 8*e - 47, -3*e^2 - 20*e + 37, -3*e^2 + 2*e + 1, 2*e^2 + 16*e + 14, 15*e^2 + 10*e - 35, -3*e^2 - 10*e - 33, -15/2*e^2 + 2*e - 21/2, -2*e^2 - 12*e + 12, e^2 + 35, -5*e^2 - 6*e + 27, -3*e^2 - 16*e + 15, -5/2*e^2 + 2*e - 47/2, -5*e^2 + 18*e + 33, -3*e^2 + 7*e - 22, 4*e - 4, 13/2*e^2 + 6*e - 137/2, -10*e^2 - 8*e + 56, 6*e^2 + 10*e - 2, -e^2 + 18*e + 3, -3*e^2 + 2*e + 29, 7*e^2 - 4*e - 41, 8*e^2 + 3*e - 51, 13/2*e^2 + 2*e - 69/2, -5/2*e^2 + 14*e + 21/2, -18*e^2 - 16*e + 40, 6*e^2 + 15*e - 25, 6*e^2 + 4*e + 18, -16*e^2 - 6*e + 56, 4*e^2 + 10*e - 52, -7*e^2 - 16*e + 31, -8*e^2 - 10*e + 42, 8*e^2 + 16*e + 8, -3*e^2 - 12*e - 9, -7*e^2 - 20*e + 15, 7*e^2 + 24*e - 23, -9*e^2 - 16*e + 11, 1/2*e^2 + 20*e - 25/2, -19/2*e^2 + 14*e + 83/2, 12*e^2 + 38*e - 54, 21/2*e^2 + 12*e + 19/2, -13/2*e^2 - 12*e + 49/2, -8*e^2 - 8*e + 8, -17*e^2 - 36*e + 53, -17*e^2 - 22*e + 63, -3*e^2 - 8*e + 15, -5*e^2 - 16*e - 13, -5*e^2 + 4*e + 47, -6*e^2 - 4*e + 66, 13/2*e^2 - 8*e - 29/2, 10*e^2 - 62, 14*e^2 + 8*e - 62, -27/2*e^2 - 30*e + 71/2, -6*e^2 - 12*e + 74, -12*e^2 - 12*e + 66, -2*e^2 - 4*e - 28, -4*e^2 - 2*e - 10, 15*e^2 + 16*e - 55, -41/2*e^2 - 26*e + 105/2, 11*e^2 + 28*e - 33, 3*e^2 + 13*e - 38, -2*e^2 + 4*e - 36, -1/2*e^2 - 12*e + 29/2, 13*e^2 - 12*e - 57, 13/2*e^2 + 12*e - 53/2, -33/2*e^2 + 4*e + 129/2, -11*e^2 - 2*e + 27, 10*e^2 + 20*e - 68, 3/2*e^2 + 4*e - 63/2, 20*e^2 + 20*e - 66, 19/2*e^2 + 2*e - 103/2, -9*e^2 - 14*e + 43, 7*e^2 + 3*e - 44, -2*e^2 - 28*e + 20, -2*e^2 - 21*e + 35, 7*e^2 + 26*e - 37, -33/2*e^2 - 8*e + 89/2, 7*e^2 + 6*e - 39, -26*e^2 - 24*e + 70, -10*e^2 + 4*e + 22, -12*e^2 + 20, 2*e^2 + 12*e - 42, 13*e^2 - 69, 3*e^2 + 2*e - 25, -1/2*e^2 + 8*e + 61/2, 3/2*e^2 + 20*e + 57/2, 16*e^2 + 4*e - 44, 17/2*e^2 - 6*e - 9/2, -3*e^2 + 2*e - 25, 13*e^2 - 4*e - 45, 7*e^2 + 4*e - 15, 11*e^2 + 12*e - 25, -7*e^2 - 6*e - 29, 7*e^2 + 26*e - 27, 27/2*e^2 + 12*e - 87/2, -8*e^2 + e + 31, 17*e^2 - 81, -e^2 - 9*e - 20, 6*e^2 - 16*e - 12, e^2 + 22*e + 5, 6*e^2 + 8*e + 42, 3/2*e^2 + 8*e - 59/2, 9/2*e^2 + 20*e - 85/2, 25/2*e^2 + 8*e - 13/2, e^2 + 22*e + 5, -17*e^2 - 8*e + 61, -10*e^2 + 16*e + 66, -33/2*e^2 - 8*e + 109/2, 5*e^2 - 16*e - 55, 12*e^2 + 24*e - 32, -10*e^2 + 20*e + 58, 8*e^2 + 8*e - 66, -17/2*e^2 + 6*e + 17/2, 22*e^2 + 5*e - 71, -25/2*e^2 - 8*e + 57/2, 10*e^2 + 8*e - 40, -15*e^2 - 10*e + 19, -8*e^2 - 24*e + 34, 8*e^2 - 8*e - 38, 15*e^2 + 19*e - 4, e^2 - 10*e - 21, 17*e^2 + 14*e - 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82, -11*e^2 - 12*e + 23, -3/2*e^2 + 46*e + 71/2, 37/2*e^2 + 7/2, 6*e^2 + 25*e - 27, -19/2*e^2 - 10*e - 45/2, -9*e^2 + 4*e - 11, -63/2*e^2 - 40*e + 267/2, -39*e^2 - 27*e + 120, -48*e - 38, -7*e^2 - 31*e + 20, 20*e^2 + 8*e - 10, 12*e^2 - 12*e - 124, 5/2*e^2 - 10*e + 31/2, -7/2*e^2 + 2*e + 67/2, 15*e^2 + 4*e - 39, 9*e^2 - 26*e + 15, 41/2*e^2 + 18*e - 141/2, 24*e^2 + 24*e - 66, -3*e^2 - 15*e - 56, -17*e^2 - 40*e + 45, -26*e^2 - 48*e + 90, -32*e^2 - 28*e + 102, 25*e^2 + 67*e - 146, -6*e^2 - 34*e + 50, -28*e^2 - 18*e + 140, -2*e^2 - 4*e + 8, 13*e^2 - 26*e - 61, -36*e^2 - 78*e + 132, 7*e^2 + 37*e + 30, -18*e^2 - 28*e - 16, 10*e^2 + 30*e - 22, -37/2*e^2 - 30*e + 237/2, -55/2*e^2 - 24*e + 163/2, 18*e^2 - 8*e - 50, -e^2 - 68*e - 19, 16*e^2 - 8*e - 30, -5*e^2 - 26*e - 67, 11/2*e^2 + 32*e - 51/2, 20*e^2 + 4*e - 22, -9*e^2 + 16*e - 9, -11*e^2 + 16*e + 89, -33/2*e^2 - 8*e + 65/2, -30*e^2 - 4*e + 122, -43*e^2 - 42*e + 95, -6*e^2 - 20*e - 44, -21/2*e^2 - 50*e + 5/2, -11/2*e^2 - 48*e - 117/2, -67/2*e^2 - 12*e + 203/2, -e^2 - 40*e - 27, 5*e^2 - 20*e - 53, 9*e^2 + 28*e - 93, 9/2*e^2 + 56*e + 39/2, -7*e^2 - 10*e - 39, -7*e^2 + 4*e - 29, 7/2*e^2 - 32*e - 151/2, 20*e^2 - 50, -5*e^2 + 18*e + 21, 15*e^2 + 14*e - 43, 44*e^2 + 32*e - 138, -99/2*e^2 - 34*e + 279/2, -49/2*e^2 - 26*e + 221/2, -30*e^2 - 34*e + 60, 4*e^2 + 44*e + 60, 33/2*e^2 + 24*e + 27/2, 13*e^2 + 36*e - 101, 37*e^2 + 14*e - 167, 14*e^2 - e - 125, -35/2*e^2 - 28*e - 9/2, 9/2*e^2 - 14*e + 111/2, 8*e^2 - 16*e - 24, -81/2*e^2 - 34*e + 213/2, 6*e + 36, -2*e^2 + 2*e + 126, 19/2*e^2 + 40*e - 215/2, -7*e^2 - 20*e + 101, 6*e^2 - 27*e - 19, 18*e^2 + 60*e - 38, 19*e^2 + 24*e - 141, -9*e^2 - 6*e + 61, -17/2*e^2 - 46*e + 57/2, 1/2*e^2 + 20*e + 119/2, 29/2*e^2 + 30*e + 39/2, 28*e^2 + 35*e - 147, -8*e^2 + 24*e + 80, 3*e^2 + 40*e + 13, 14*e^2 + 64*e - 10, -8*e + 12, 46*e^2 + 30*e - 166, 9/2*e^2 - 2*e - 73/2, 81/2*e^2 + 52*e - 317/2, -19*e^2 + 43, -2*e^2 - 32*e + 48, -1/2*e^2 - 4*e - 79/2, -35*e^2 - 30*e + 115, 38*e^2 + 34*e - 114, 3*e^2 - 34*e - 27, -8*e^2 - 36*e + 98, -12*e^2 - 43*e + 7, 39/2*e^2 + 50*e - 231/2, 28*e^2 + 48*e - 74, 25*e^2 + 18*e - 97, 15*e^2 + 20*e + 33, 11*e^2 + 24*e + 77, -6*e^2 - 96, -3*e^2 + 21*e - 36, -23*e^2 - 16*e + 127, -8*e^2 + 34*e - 18, 43*e^2 + 26*e - 143, -17*e^2 - 17*e - 4, 24*e^2 + 40*e - 8, 41/2*e^2 + 74*e - 257/2, 20*e^2 - 8*e - 84, 11/2*e^2 - 24*e + 69/2, -31*e^2 + 16*e + 141, 9*e^2 + 10*e - 41, 99/2*e^2 + 60*e - 327/2, 35*e^2 + 12*e - 139, 25*e^2 + 46*e - 129, -5/2*e^2 - 67/2, -18*e^2 + 34*e + 104, -e^2 + 12*e - 43, -20*e^2 - 46*e + 52, -28*e^2 - 20*e + 66, -5/2*e^2 - 22*e - 107/2, -8*e^2 - 15*e + 75, 9*e^2 + 24*e - 75, 37*e^2 + 14*e - 157, -16*e^2 - 43*e - 25, -4*e^2 - 28*e - 48, 3*e^2 + 15*e - 112, 27*e^2 + 48*e - 37, 43/2*e^2 + 30*e - 239/2, -36*e^2 - 38*e + 132, -37*e^2 - 22*e + 149, -17*e^2 - 44*e + 55, 13*e^2 + 42*e - 65, -23*e^2 + 23*e + 126, -9*e^2 + 24*e + 53, 35/2*e^2 - 38*e - 259/2, -15*e^2 + 38*e + 73, -e^2 - 16*e - 11, -22*e^2 - 36*e + 74, 36*e^2 + 20*e - 76, 37/2*e^2 + 64*e - 249/2, -19*e^2 - 24*e + 157, -21*e^2 - 37*e + 32, 14*e^2 + 28*e + 32, 2*e^2 - 24*e + 2, -12*e^2 - 28*e + 40, 95/2*e^2 + 50*e - 219/2, -91/2*e^2 - 12*e + 287/2, -4*e^2 - 40, -17/2*e^2 + 8*e + 193/2, 1/2*e^2 + 52*e + 39/2, 4*e^2 + 20*e - 96, -18*e^2 + 2*e + 66, 28*e^2 + 88*e - 146, 29*e^2 + 16*e - 65, 2*e^2 + 4*e - 66, 19*e^2 + 50*e - 99, 1/2*e^2 + 4*e + 231/2, -12*e^2 - 28*e, -11*e^2 + 48*e + 63, 24*e^2 + 26*e - 90, -99/2*e^2 - 72*e + 291/2, 15*e^2 + 22*e - 139, 24*e^2 + 30*e - 124, -25/2*e^2 + 2*e - 147/2, -6*e^2 + 24*e + 92, 15*e^2 + 34*e - 123, -10*e^2 - 30*e + 134, 11*e^2 + 22*e - 65, 4*e^2 + 28*e - 40, -63/2*e^2 - 20*e + 183/2, 12*e^2 - 14*e - 48, -61/2*e^2 - 18*e + 105/2, -13*e^2 + 22*e + 85, 23/2*e^2 + 34*e + 93/2, 49*e^2 + 52*e - 135, -17/2*e^2 - 14*e - 95/2, 22*e^2 + 47*e - 105, -30*e^2 + 25*e + 173, -28*e^2 - 40*e + 100, e^2 + 4*e - 129, 15*e^2 - 24*e - 71, -53/2*e^2 + 12*e + 205/2, -9*e^2 - 32*e + 117, -20*e + 30, -7*e^2 - 18*e + 67, 12*e^2 + 34*e - 26, -45*e^2 - 44*e + 81, -27*e^2 - 14*e + 73, -15*e^2 + 10*e + 93, 11/2*e^2 + 38*e - 107/2, -7/2*e^2 - 2*e + 135/2, 19*e^2 - 42*e - 73, -30*e^2 + 8*e + 118, -23/2*e^2 + 26*e + 191/2, 81/2*e^2 + 28*e - 317/2, -63/2*e^2 - 80*e + 207/2, 11*e^2 + 4*e + 9, 39/2*e^2 + 42*e - 179/2, 5*e^2 - 42*e - 97, 35/2*e^2 + 56*e - 95/2, e^2 - 60*e - 61, 49/2*e^2 - 8*e - 209/2, -e^2 - 12*e - 133, 5*e^2 + 13*e - 44, -28*e^2 + 4*e + 170, -18*e^2 - 18*e + 180, -29/2*e^2 + 14*e + 5/2, -21/2*e^2 - 64*e + 149/2, 41*e^2 - 2*e - 135, -22*e^2 - 12*e + 132, 43*e^2 + 38*e - 63, 11*e^2 - 6*e + 71, -46*e^2 - 36*e + 94, 3*e^2 - 34*e + 57, -6*e^2 + 40*e + 96, 39*e^2 + 62*e - 97, 20*e^2 + 30*e - 10, -31/2*e^2 - 6*e + 75/2, -65/2*e^2 - 30*e + 185/2, -37/2*e^2 + 12*e + 221/2, -26*e^2 - e + 147, 8*e^2 - 6*e - 92, -11/2*e^2 - 40*e - 57/2, -24*e^2 - 6*e - 8, 3*e^2 - 49*e - 52, -15*e^2 - 14*e - 41, 16*e^2 + 20*e - 2, 71/2*e^2 + 34*e - 139/2, 46*e^2 + 25*e - 187, -31/2*e^2 - 4*e + 263/2, -21*e^2 + 24*e + 97, -13*e^2 - 26*e + 113, -9/2*e^2 + 8*e + 229/2, -14*e^2 - 7*e - 19, -3*e^2 + 10*e - 19, -13*e^2 - 60*e + 95, -15*e^2 + 14*e + 11, -4*e^2 - 25*e - 7, 11/2*e^2 - 10*e - 55/2, 12*e^2 + 42*e - 82, -23*e^2 - 86*e + 97, -37*e^2 - 24*e + 139, 17*e^2 + 6*e - 37, 45/2*e^2 + 30*e + 35/2, 37*e^2 + 40*e - 133, 33/2*e^2 + 16*e - 65/2, -35*e^2 + 12*e + 163, -31*e^2 + 6*e + 115, 3*e^2 + 8*e + 3, 11*e^2 + 16*e + 113, -28*e^2 + 20*e + 112, -2*e^2 - 18*e - 150, 28*e^2 + 28*e + 2, -23/2*e^2 + 28*e + 123/2, 15*e^2 - 30*e - 133, -35*e^2 - 41*e + 70, 30*e^2 - 44*e - 156, 51/2*e^2 + 40*e - 95/2, -32*e^2 - 19*e + 147, 9*e^2 + 17*e - 60, 54*e^2 + 24*e - 156, 19*e^2 + 52*e - 143, 53/2*e^2 + 18*e + 23/2, 22*e^2 + 32*e - 42, -42*e^2 - 44*e + 102, 18*e^2 - 52*e - 156, -24*e^2 - 30*e - 4, 12*e^2 + 46*e - 46, -16*e^2 - 42*e + 110, -17*e^2 - 53*e + 132, 8*e^2 - 4*e - 90, 5*e^2 - 29*e - 130, 9*e^2 + 20*e - 43, 2*e^2 - 28*e + 26, 5/2*e^2 + 34*e - 29/2, 15*e^2 - 133, -8*e^2 + 32*e + 58, -105/2*e^2 - 26*e + 369/2, 28*e^2 + 60*e - 48, 20*e^2 + 19*e + 61, 23*e^2 + 58*e - 53, 25/2*e^2 + 22*e - 197/2, 7/2*e^2 + 22*e - 75/2, 24*e^2 + 54*e - 106, 20*e^2 + 60*e - 28, 4*e^2 - 8*e - 74, -18*e^2 - 14*e + 82, 37*e^2 + 39*e - 106, -8*e^2 - 70*e + 16, -27*e^2 + 4*e + 131, -22*e^2 - 42*e + 144, 17/2*e^2 - 24*e - 113/2, 17*e^2 - 54*e - 113, 39*e^2 + 32*e - 155, 43/2*e^2 + 36*e - 239/2, -41*e^2 - 28*e + 121, 3*e^2 + 50*e + 11, -7*e^2 - 23*e - 28, -e^2 - 16*e - 13, 23/2*e^2 + 8*e + 201/2, -26*e^2 - 58*e + 116] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([79, 79, -w - 9])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]